2 Answers
2

You got the reported result for
apt-get install apt-cache because there is no package called apt-cache.
The following commands are part of apt package:apt-cache, apt-cdrom, apt-config, apt-get, apt-key, apt-markCourtesy: Ubuntu software center

Since apt-get itself is working for you, the apt package and therefore apt-cache command should be installed in your system. So no need for manually installing it.

Try apt-cache show apt to ensure that your apt-cache command is working.